Causal inference (CI) has recently been proposed as a universal computational motif in the brain [Shams \& Beierholm 2020]. However, how CI is implemented by neural circuits, and its signatures in terms of single neuron responses, are still unclear. We have investigated this question in the context of complex motion processing. Motion perception deviates from retinal motion [Johansson 1973] a computation that can be understood in terms of hierarchical CI over which moving elements to integrate into coherent 'groups' vs segment into different ones [Gershman et al. 2016, Shivkumar et al. 2020]. Yet, most of our understanding of the neural basis of motion processing is in terms of retinal motion, delegating potential CI computations to downstream cortical areas [Rohe et al. 2015, 2019]. Our work makes two contributions: first, we present new psychophysical evidence for the hierarchical nature of this process using a display of hierarchically nested groups of moving dots. Second, we use the hierarchical CI model fit to psychophysical data to derive quantitative neural predictions for neurons representing the variables in our model. At each level, our model contains two types of variables: one that represents the retinal motion predicted by the larger surround, and one that represents the difference between the actual local motion and that predicted from the surround. The predicted neural responses show remarkable similarity to two classes of neurons found in area MT: neurons with suppressing and with reinforcing surrounds [Born \& Bradley 2005]. Finally, we present new neurophysiological data from area MT in a macaque monkey where the velocity-dependent pattern of surround suppression of neural responses agreed with that predicted for the relative variable in our CI model. Our results show that signatures of CI are already present at the early stages of sensory processing, and suggest that they may be implemented by local computations.